1. Field of the Invention
The present invention relates to a Wien filter (E×B filter) used in an energy filter for use in an electron microscope, mass filter, spin rotator, monochrometer, energy analyzer, or the like. The present invention also relates to an electron microscope using such a Wien filter.
2. Description of Related Art
Accelerated charged particles, such as electrons, are deflected toward positive poles with respect to an electric field. With respect to a magnetic field, the particles are deflected perpendicular to the direction of travel of the particles and to the magnetic field. A Wien filter makes use of these phenomena and uses electric and magnetic fields that are placed perpendicular to each other within a plane perpendicular to the direction of travel of the charged-particle beam. The beam is made to move straight in a certain direction.
The condition under which a charged-particle beam goes straight through a Wien filter is known as the Wien condition and given byE1=vB1where E1 is the first-order component (dipole component) of the electric field, B1 is the first-order component (dipole component) of the magnetic field, and v is the velocity of the charged particles.
It has been considered that the Wien condition can be satisfied within the inner area excluding the vicinities (known as fringing fields) of the entrance and exit for the beam, for the following reason. Where the electrodes and magnetic polepieces are different in geometry, the electric and magnetic fields are different in distribution and, therefore, the Wien condition holds in some locations but does not in other locations. The magnetic pole pieces may be hereinafter often referred to as magnetic poles or simply as poles.
A Wien filter in which electrodes and magnetic polepieces are identical in geometry has been proposed by Tang (Optik, 74, No. 2 (1986), pages 51-56, “Aberration Analysis of a Crossed-Field Analyzer”, Tian-Tong Tang). This is an octopole filter, and the electrodes and magnetic polepieces are identical in geometry. Therefore, the problem that the fringing fields do not satisfy the Wien condition can be circumvented. Hence, a Wien filter having theoretically expected performance can be accomplished.
However, when the Tang's filter is put into practical use, a drawback occurs. The filter has eight poles that are used as individual electrodes and magnetic polepieces. These electrodes and magnetic polepieces create their respective dipole and quadrupole components. In consequence, a number of power supplies are necessary. In practice, Wien filters are often used floating on high voltages to provide large dispersion. It is not practical to place a number of power supplies in locations at high electric potentials. For these reasons, the Tang's filter has not been put into practical use.
On the other hand, we have proposed a practical octopole filter (Japanese Patent No. 3040245), which is shown in FIG. 9, (a) and (b). This filter has greater poles P1, P3, P5, and P7 and smaller poles P2, P4, P6, and P8, i.e., eight poles in total. The poles P2, P3 and P4 together form a magnetic pole pair via a coil C1. Similarly, the poles P6, P7 and P8 together form a magnetic pole pair via a coil C2. The poles P2, P1 and P8 together form an electrode pair. Similarly, the poles P4, P5 and P6 together form an electrode pair.
The poles P2, P1, and P8 are fabricated integrally. Similarly, the poles P4, P5, and P6 are fabricated integrally. The poles P2, P4, P6, and P8 are bent at their intermediate locations to facilitate winding the coil C1 between the poles P2 and P4 across the pole P3 and winding the coil C2 between the poles P6 and P8 across the pole P7.
Because of this arrangement of the electrodes and magnetic polepieces, the Wien filter can be operated with only three input terminals and three power supplies. One of the three input terminals is used to supply current into the coils C1 and C2 at ground potential. Another input terminal is used for a positive voltage. The remaining input terminal is used for a negative potential. It is known that stigmatic focusing can be achieved under the condition                                                         E              2                                      E              1                                -                                    B              2                                      B              1                                      =                              -                          1              4                                ⁢                      R            0                                              (        1        )            where E2 is the quadrupole component of the electric field, B2 is the quadrupole component of the magnetic field, and R0 is the cyclotron radius of the charged particles where the magnetic field exists alone and given by                               R          0                =                              mv            2                                eE            1                                              (        2        )            where v is the velocity of the charged particles, m is the mass of the charged particles, and e is the charge of the charged particles.
A quadrupole electric field for achieving stigmatic focusing by satisfying the above-described condition may be realized also by varying the ratio of the absolute values of voltages applied to the poles P2, P1, P8 and to the poles P4, P5, and P6, but this is not strictly true. Therefore, it is better to fulfill the condition by producing a quadrupole electric field using four poles P1, P3, P5, and P7 (i.e., with addition of the poles P3 and P7).
These circumstances are described in detail in J. Electron Microsc., 45, pages 417-427 (1996), “Simulation of Electron Trajectories of Wien Filter for High-Resolution EELS Installed in TEM” (K. Tsuno and J. Rouse).
In the Wien filter (octopole filter) described in the above-cited Japanese Patent No. 3040245, the electrodes are exactly identical in geometry with the magnetic polepieces. Therefore, charged particles are not deflected at the fringes. In practice, the instrument has been put into practical use as a monochrometer, and has excellent ease of use. However, it has still been difficult to reduce the aberration down to zero. Generally, a Wien filter has a considerably large amount of second-order aberration. Where it is used as a monochrometer, the size of the charged-particle beam going out of the filter is greater than that of the beam yet to enter the filter.
With respect to the second-order aberration of the Wien filter, H. Rose has already shown a condition capable of making it zero (Optik, 77, No. 1 (1987), pages 26-34, “The retarding Wien filter as a high-performance imaging filter”, H. Rose).
This condition is given by Eqs. (3) to (9).                               e          2                =                  -          1                                    (        3        )                                          b          2                =                  -                      3            4                                              (        4        )                                                                    e              3                        -                          b              3                                =                      3            8                          ⁢                                  ⁢        where                            (        5        )                                          e          2                =                              (                                          E                2                                            E                1                                      )                    ⁢                      R            0                                              (        6        )                                          b          2                =                              (                                          B                2                                            B                1                                      )                    ⁢                      R            0                                              (        7        )                                          e          3                =                              (                                          E                3                                            E                1                                      )                    ⁢                      R            0            2                                              (        8        )                                          b          3                =                              (                                          B                3                                            B                1                                      )                    ⁢                      R            0            2                                              (        9        )            where E1 and B1 are the dipole components of the electric and magnetic fields, respectively, E2 and B2 are quadrupole components of the fields, respectively, E3 is the high-order inhomogeneous component of the electric field E1, B3 is the high-order inhomogeneous component of the magnetic field B1.
Among these conditions, e2 and b2 can be achieved relatively easily, for the following reason. The condition for achieving stigmatic focusing is expressed by Eq. (1) and given by                     E        2                    E        1              -                  B        2                    B        1              =                    e        2            -              b        2              =                  -                  1          4                    ⁢              R        0            Therefore, it suffices to determine the relation between e2 and b2 so as to satisfy this condition.
With respect to e3 and b3, we have made a simulation to know the value of the high-order inhomogeneous component E3 of the electric field in the above-described octopole filter. In this simulation, a numerical computation method known as boundary element method (BEM) was used. In particular, geometric parameters of the Wien filter (i.e., radius R of the cylindrical portion within the XY-plane perpendicular to the direction of travel of the charged particles, angular positions of the poles, polar interval, and length L0 taken in the direction of the Z-axis) were calculated. Various conditions including voltages for producing the dipole and quadrupole fields were established. The distributions of the potentials φ of the dipole and quadrupole fields and of the hexapole field parasitic to the dipole field were calculated. The dipole, quadrupole, and hexapole fields are respectively given by (dipole field):φ1=φ0−E1x+(1/8)E1″(x3+y2x)+  (10)where       E    1    ″    =                    ∂        2            ⁢              E        1                    ∂              z        2            (quadrupole field):φ2=−{E2−(1/12)E2″(x2+y2)}(x2−y2)+  (11)(hexapole field):φ3=−E3(x3+3xy2)+  (12)Therefore, the electric field potential φ on the x-axis, for example, is given byφ=φ1+φ2+φ3+ . . . =φ0−E1x+E2x2−(1/8)E1″x3−E3x3+(1/12)E2″x4+  (13)
In the foregoing, it is assumed that the radius R of the cylindrical portion is 5 mm, L=40 mm, and accelerating voltage is 2.5 kV. Furthermore, the dipole electric field=1651.1734 V, quadrupole electric field=280.7162 V, dipole magnetic field=44.3101 AT, and quadrupole magnetic field=6.5412 AT.
FIGS. 8(a) and 8(b) show the distribution of the high-order inhomogeneous component E3 along the optical axis where a dipole electric field of 1 V is applied. As can be seen from this graph, the high-order inhomogeneous component E3 has a high value of 12000 V/m3 in the fringing fields. In FIG. 8(a), the horizontal axis indicates the direction of travel (Z-axis direction) of charged particles through an octopole Wien filter shown in FIG. 8(b). The vertical axis indicates the high-order inhomogeneous component E3 of the electric field.
It is possible to reduce the high-order inhomogeneous component E3 close to zero outside the fringing fields by adjusting the angular positions of the poles. However, the component stays at large values in the fringing fields and cannot be reduced to a small value. The same situation applies to the high-order inhomogeneous component B3 of the magnetic field. Therefore, the conventional Wien filter has the problem that the second-order aberration cannot be reduced.